Britain remained in the grip of severe icy weather today, with plunging overnight temperatures creating travel chaos and widespread disruption in the final countdown to Christmas.

Thousands of commuters were expected to heed police advice to stay off the roads, while the UK's main airports warned that they were only able to run a limited number of flights.

The Christmas travel plans of thousands of families were in disarray as stranded passengers slept on the floors of terminals at Heathrow airport for a second night.

There were just seven flights from the airport yesterday and, although one runway was open from 6am this morning, passengers were told there would be cancellations and delays over the coming days, with many aircraft crew and planes in the wrong places.

British Airways said it expected 60 flights to take off today, but added that a further 80 had been cancelled.

Colin Matthews, the chief executive of the airport's owner, BAA, said: "We need to find better ways of communicating to thousands of people."

Speaking on BBC Radio 4's Today, he added: "We are set up for snow and ice, but if we have to face week upon week of subzero temperatures, then we will have to think again."

The company had 70 different types of snow plough, but would "have to look again at all of this in the coming weeks", he said.

Temperatures fell to -19.6C in Chesham, Buckinghamshire, overnight, while Northern Ireland saw a record low of -17.6C in Castlederg, Co Tyrone.

Severe weather warnings were in place for the whole of southern England and Wales, with a warning of up to 20cm of fresh snow in the south-west this morning.

Rush hour traffic was hit by blizzards in Devon, which brought the A30 and A38 to a standstill, with gritters stuck behind stranded cars.

Devon and Cornwall police said no journey was essential enough for anyone to be out on the roads, and advised delaying journeys for at least a few hours.

The band of snow is expected to hit the south-east later, while the Midlands and northern England are being affected by freezing fog.

Steve Willington, a Met office forecaster, said: "Snow, combined with widespread ice and freezing temperatures will lead to the risk of significant disruption through Monday."

Train companies were attempting to run near-normal services. The busy Southeastern and Southern commuter franchises warned of some delays and cancellations but said they were running normal timetables, while South West Trains said it was running an amended service.

Overhead wire problems were causing delays on the east coast mainline into London King's Cross.

But Eurostar was recommending that passengers cancel or postpone their journeys after the weather caused a huge backlog over the weekend.

More than 1,000 passengers, including hundreds of Britons, were stranded at Gare du Nord station in Paris last night after Eurostar cancelled at least eight rail services, switching to a contingency timetable after France was also hit by severe weather.

This morning there were still long queues, but travellers said they were moving and weekend passengers were being given priority.

The motorway network and main trunk routes throughout Britain were open, but icy surfaces were creating hazardous conditions in most areas. An overturned vehicle meant the M4 was closed westbound in west London early today.

The Highways Agency said it was doing its best to keep roads in England clear, but its spokesman Jon Caudwell added that motorists should "really seriously consider" whether they needed to go out.

Calls were coming in to the AA at a rate of 800 an hour. The organisation's president, Edmund King, warned that many roads were still treacherous and urged the highway authorities to "plough and grit" as many as possible.

Royal Mail pledged up to 14,000 extra delivery rounds – weather permitting – to 2m homes over the next four evenings in an attempt to clear the huge Christmas postbag.

Retail experts warned of empty supermarkets if conditions did not improve, with deliveries struggling to get through. Howard Archer, the chief UK economist at IHSGlobal Insight, said: "If this weather persists, it is going to be very disruptive to deliveries to supermarkets.

"Supply chains have been massively hit by the snow and ice this month, with many products being stuck at container ports for an extended period."

The treacherous conditions are believed to have played a part in the deaths of at least three people in recent days.

The transport secretary, Philip Hammond, rejected charges of complacency from Labour and said the government was consulting its chief scientific officer over whether long-term investment was required.

Angela Eagle, the shadow chief secretary to the Treasury, accused the government of being "caught asleep on the job" while the shadow chancellor, Alan Johnson, was scathing about the government's response.

People were being told to "get a shovel or stay at home", he said, adding that salt supplies were arriving in "dribs and drabs" when "they should have been here now".

But Hammond argued that providing "absolute certainty" of no disruption would cost vast sums. If such extreme weather were to be more regular, some major improvements could be made, he added.

A government-ordered review on measures for coping with a prolonged freeze, by David Quarmby, the chair of the RAC Foundation, is due to be published tomorrow.